Method for correcting errors by de-embedding dispersion parameters network analyst and switching module

ABSTRACT

The invention relates to a method for correcting errors by de-embedding scattering parameters of a device under test associated with measuring ports ( 11 ), the parameters being measured by a vector network analyzer including n measuring ports. The aim of the invention is to create a universal, precise and fast method of correcting errors of scattering parameters. To this end, the method includes the following steps: formula ( 1 ) two-port calibrations are carried out on different calibrating standards in any order in the active state between the measuring ports ( 11 ), as a basis for a first error correction; the reflection parameters of at least one part of the n measuring ports ( 11 ) are determined in the inactive state, by way of the results of two-port measurements carried out on at least one calibrating standard switched in the active and/or inactive state on measuring ports ( 11 ), as a basis for a second error correction. The invention also relates to a network analyzer and to a switching module for a network analyzer.

BACKGROUND OF THE INVENTION

The invention concerns a procedure for error correction by thede-embedding of a scattering parameter, which has been measured with ann-port containing, vectorial network analyzer, wherein the scatteringparameter relates to a device under test connected to the said ports.The invention also concerns a vectorial network analyzer for the saidprocedure as well as a circuit module for the said network analyzer.

In high frequency technology, the behavior of circuits is normallydescribed in terms of scattering parameters. The scattering parametersrepresent complex reflection and transmission parameters of a circuitand join ingoing and outgoing waves with one another. A representationof this type where complex reflection and transmission parameters areconcerned is especially well suited to the physical realities of theproblems brought forth in high frequency technology.

Thus, for example, a circuit, which is formed by a linear 2-port, and isincorporated in the scattering parameters by means of its scatteringmatrix [S], can be completely described. If the waves, whichrespectively run to one port of the 2-port, are designated as a₁ and a₂and those waves which depart from respectively one port of the 2-port,and propagate themselves in a reverse direction, are designated by b₁and b₂, then, for the scattering matrix [S] the following validrelationship serves:

$\begin{pmatrix}b_{1} \\b_{2}\end{pmatrix} = \underset{\underset{= {\lbrack S\rbrack}}{︸}}{\begin{pmatrix}S_{11} & S_{12} \\S_{21} & S_{22}\end{pmatrix}\begin{pmatrix}a_{1} \\a_{2}\end{pmatrix}}$Experience in the practice allows it to be known, that for thedetermination of the scattering parameter, it is advantageous to employa circuit of a network analyzer to which the circuit of the device undertest can be connected. By means of such a network analyzer, the wavesapproaching the device under test are input and captured at themeasurement positions. Likewise, the waves sent in the oppositedirection are captured at measurement positions. From these measuredvalues, it is then possible to determine the scattering matrix [S].

The goal of every n-port measurement by means of a network analyzer isto determine the scattering parameter with the greatest precision. Inany case, error interferences occur throughout the network analyzeritself, such as, for example, improper interlinkage or mismatching,which falsify the results of measurements.

The precision of the measuring capacity of the network analyzer, can besubstantially improved by a system error correction. Where the systemerror correction is concerned, measurement takes place within acalibration process, this being the so-called calibration standards,that are devices under test, which are partially or fully known. Fromthese measurement values and through special computational paths, oneobtains correction data. With these correction data and a correspondingcorrection computation, one obtains for each device under test from therough measurement values, corrected scattering parameters, which arethen free from the said system error of the network analyzer.

De-embedding is to be understood as a situation wherein after acalibration has been made as described, one has obtained scatteringparameters, which are not yet sufficiently error-free, and subsequentlythe said scattering parameters are subjected to a second measurementcorrection. This can be, in the simplest case, a multiplication with aninverse chain matrix of a known circuit line between the networkanalyzer and the device under test. As a rule, a good calibration in thereference planes of the device under test is more exact than anadditional de-embedding step. However, a calibration is often timeconsuming and complex, and in many cases the exactness of a de-embeddingstep is sufficient. In the literature, de-embedding is designated as a“Two-Tier-Calibration”, which also makes clear, that when de-embeddingis practiced, a two-stage calibration, i.e. a two-stage error-correctivemeasure of the raw measured values is being undertaken.

Principally, network analyzers are a means of measuring electronicequipment of one and 2-port parameters in a range of, for instance,electronic semiconductor components to antennas. These 1-port and 2-portcalibration procedures form, however, no fully sufficient basis forerror correction in the measurement of multiport objects. One problemwith multiport measurement is found therein, in that, namely all portsof the device under test are interlinked.

Thus, one cannot obtain, from a single point of measurement, a value forthe waves departing, then at the next measuring point, achieve a valuefor the reflected wave, and finally at a third measurement point, pickup a value for a transmitted wave, which value would be independent ofthe connection terminals of the multiport device.

However, for several years, network analyzers with a nearly optionallylarge number n of measuring ports have been put to use for the detectionof the complex reflection and transmission characteristics of multiportdevices under test. Procedures in accord with this have been describedin the documents DE 199 18 697 A1 and DE 199 18 960 A1. DE 199 18 960 A1is based on the use of a 7-term-procedure for 2-port measuring, and DE199 18 697 A1 is based on the use of a 10-term procedure for 2-portmeasuring. The calibration procedures presented in the saiddocumentation for the error module for n-port network analyzers aredirect multiport calibration procedures, which, to be sure, are exact,but however, with which, in practice, the necessary measurements andcorrections are very time consuming. The result of this is, that theseprocedures cannot be employed for network analyzers, which exhibit threeor four measurement positions, which by means of two inner ports and acircuit matrix are connected with the ports of the device under test.These network analyzers present, however, by far the largest group ofapplied network analyzers.

In modern network analyzers with four measuring positions, there hasbeen one in the dissertation publication “Safe Procedure for theCalibration of Network Analyzers for Coaxial and Planar Line Systems”,Institute for High Frequency Technology, Ruhr University, Bochum, 1995,from H. Heuermann's descriptive TRL, i.e. “Through Line ReflectanceCalibration Procedure”. In this procedure, there is required, aside fromthe through connection T, the remaining two standards L and R, whichneed be only partially known. In the said publication, however, it hasbeen shown, that the TRL-procedure can be seen as essentially a specialcase of a general theory for the so-called “two error matrix 2-portmodel”.

As devices under test of multiport measurements, first, there is aseries of objects with unsymmetrical terminal connections (as a rule, 50Ω-ports) such as couplers, signal parts, and frequency selectivefilters, and second, objects to be considered with connection terminalsof various types, such as, for instance, symmetrical members andSAW-filters (i.e., Surface Acoustic Wave filters). In the case of thelatter, the state of the technology is, that the differential mode, bymeans of an additional working step under the limitations of an idealtransformer is retroconverted into an unsymmetrical mode.

Thus, the invention has the purpose of making available a procedure, anetwork analyzer and a circuit module, which permit a universallyapplicable, exact and non-time consuming error correction of thescattering parameters of a device under test, as measured by means of anetwork analyzer.

SUMMARY OF THE INVENTION

Between the pairs of n ports of a network analyzer, by appropriateconnection, a calibration standard signal path can be formed. Where nports are concerned,

$k = {n \cdot \frac{n + 1}{2}}$various combinations of pairs of ports are possible, and therewith, alsok of such signal paths per pair of ports. The necessary capture meansfor the 2-port calibration from signals approaching the ports, and thosesignals emitted from the ports can be optionally constructed. Thus, then ports of the network analyzer can be connected both by a circuitmatrix and inner ports with 3 or 4 measuring positions, as well as beingconnected by only one switch matrix with 3, 4 or n−1 measuringpositions, and as well, even without a switch matrix directly to 2·nmeasuring positions.

Calibration standards may be established as in the known calibrationprocedures involving n-ports, 2-ports, and/or single to n times ports,which, with one exception, are advantageously completely known, or areself-calibration. As is discussed in greater detail in the above saiddissertation document, standards with self-calibration capabilities are,at this time, only based on 2-port standards, which are measured with atleast 4 measuring positions. The exception mentioned above consists, asin the known 2-port calibration procedure, of at least one, required2-port, limited transmission damping, which is not advantageouslycompletely known or is self-calibration.

If, however, the transmission damping of this 2-port becomes known,then, correspondingly installed n-times single ports need not becompletely known. The n-times 1-ports, which are capable of beinginstalled in the invented procedure and in the invented network analyzerwith the rank of a calibration standard, can be either an n-portconsisting of n 1-ports, or a 1-port which is connected and measured ateach of the n-ports.

The invention bases itself on the 2-port calibration procedureimplemented in known network analyzers. After such a known calibrationprocedure for the availability of error terms for a first errorcorrection has been carried out, the invention allows, by means of avery simple, additional de-embedding step with only a few measurements,the obtaining of exact multiport values, which give indications on themultiport behavior of the device under test.

For each port, various reflection factors exist for various conditions.Active states are given, when the port is switched to send or receive.An inactive port exists, when the port is shut off. The known 2-portcalibration procedures determine and make use of exclusively thereflection parameters of 2-port in the active state. Thereby, in anycase, the correlations between the n-ports cannot be taken intoconsideration, which determine the multiport behavior of the deviceunder test.

The proposed de-embedding step is found therein, in that after a knownk-times 2-port calibration, the reflection factors of at least some ofthe n-ports of the network analyzer are to be determined in the shutoffcondition. This determination is executed with the results of the 2-portmeasurements on at least one calibration standard connected at the portsin the active and/or the inactive state.

For network analyzers, which principally possess three or four measuringpositions, which are connected by two inner ports with the n measurementports, the inactive and the active reflection behavior of the ports aredifferent. In the case of such network analyzers the inactive reflectionfactors are determined, while respectively, on the sender side thereflections of the 2-port are measured. During this time, the port,which functions otherwise as a receiver, is shut off. Additionally, ifthe measured inactive reflection factors are freed of error, then,particularly because of the connected calibration standard between theports the measured factor diverts from the actually inactive reflectionfactor. In this case, the 2-port are additionally measured in bothdirections with the same calibration standard, while respectively; oneport is a sender and the other port functions as a receiver.Furthermore, both ports are switched to the active state. Themeasurement results can then be applied to extinguishing the error ofthe measured inactive reflection parameter.

For network analyzers, which exhibit 2·n or n+1 measuring positions, theactive and the inactive reflection behaviors of the ports are identical.On this account, in this case it becomes necessary to exclusivelymeasure the 2-port, while both ports are switched to active. In regardto determined reflection parameters of the ports in the inactive state,then simply, the reflection parameter of the ports in the active statecan be used.

The determined reflection parameters of the ports in the inactive statecan then form a base for a second error correction of the scatteringparameter by which the multiport behavior can be estimated with a highdegree of precision. With the proposed procedure, messages,decontaminated of crosstalk and faulty mix can be carried out, both incoaxial systems as well as in semiconductor substrates.

Being based on the invented procedure and the invented network analyzer,that is to say, the circuit module, it is possible, from the nowavailable 2-port-solution to very rapidly convert complex multiportsolutions for the network analyzer. This requires far less loss of timethan the known multiport procedure. The invented procedure presents, inthis way, a De-embedding, Multiport Procedure (hereinafter, “DMV”),which essentially is less expensive than the known multiport calibrationprocedure based on a few calibrations. Very importantly, the inventionpermits applications on network analyzers, which have 3 or 4 measurementpositions and wherein a switching matrix is connected to the gates,which are not possible with the known multiport calibration procedure.

A particular advantage of the proposed procedure lies in the simplepossibilities of implementation in a network analyzer. Further, theprocedure has superiorities over the known multiport-calibration method,in that not all signal paths need be measured, if only one or a fewscattering parameters are being sought. For a comprehensive errorcorrection of a scattering matrix of a device under test, however, all kpossible signal paths between two ports must be measured and therefromthe reflection parameters of combined ports in the active state aredetermined.

The claims of the here presented procedure regarding the calibrationstandards are the same as in the case of known 2-port and multiportcalibration method. This is a very important aspect for the availabilityof the calibration standard and thus also for the practical applicationthereof. Since the presented procedure permits the application of a verylarge number of calibration standards, this has the result of enablingin each circuit a possibility for the precise realization of the saidstandards and thereby an entirely new perspective in the measurement ofa plurality of ports.

Even when the reflection factors of all n ports should be measured, thenumber of the necessary contacts of individual standards in the case ofthe proposed procedure is not greater than is the case with themultiport, 10-term-method from DE 199 18 697 A1. Only, in comparison tothe said multiport, 7-term-method from DE 199 18 960 A1, additionalconnections are called for.

Advantageous embodiments of the invented procedure and the networkanalyzer are evident in the subordinate claims.

In a preferred embodiment of the invented procedure, for thedetermination of the reflection factors of 2-port in the inactive state,the through connections are maintained as in the case of the established2-port calibration in accord with a known procedure, so that noadditional connection effort is necessary. However, as compared to abasic 2-port, 7-term method, a reduced connection expense is gained.Moreover, the already established results obtained from the said throughconnection calibrations of the 2-ports in the active state can be used.Depending on the network analyzer, for each reflection parameter to bedetermined of a port a further 2-port measurement with respectively aswitched off port must be carried out in the inactive state. However,essentially, much more time consuming than the measurements themselvesis the making of new connections. The invented procedure also permitsthe de-embedding step with the inclusion of carrying out theimplementation of the well known 2-port error correction procedure ineach network analyzer.

The proposed de-embedding procedure can operate with all 2-portcalibration methods in accord with the 10-term and the 7-termtechnologies, which, for example, have been described as starting pointsin the already mentioned documents DE 199 18 697 A1 and DE 199 18 960A1. For the necessary calibration measurements up to the number k, asbasis for the first error correction, it suffices if one has availablethe conventional standards for the 10 term or the 7 term procedures, forexample, TMSO, TMR, or TLR. In these acronyms,

-   -   T=through connection    -   M=known impedance    -   S=Short circuit    -   O=open circuit    -   L=Line    -   R=Reflection Standard        Advantageous concrete embodiments with the invented        combinational 2-port calibration procedure are to be found in        the subordinate claims 5 to 8.

There are four different network analyzer designs, which can beconsidered technically advantageous. In each of these designs, theinvented procedure may be applied.

As a first, and most favorable from a price standpoint, is a networkanalyzer having three measuring positions. Two of the three measuringpositions are respectively and directly joined to two inner ports, andthe third measuring position can be joined with the two inner ports by aswitch. A switching matrix connects the two inner ports of the networkanalyzer with the n outer ports and in this way realizes the k necessarysignal paths. With this design, none of the known multiport calibrationmethods may be applied.

Going beyond the above, consideration can be given to a network analyzeras a quick, but not so economically favorable design, in which the nports are connected by a switching matrix, but an inner port with n+1measuring positions is lacking. Such a rapid design, for example, ismore closely described in the DE 199 18 697 A1.

For these first two designs, in the procedure in accord with theinvention, k 2-port-10-term methods are carried out. The requirementsregarding the calibration standards are the same as that from the knownmultiport-10-term procedure of the DE 199 18 697 A1. What is new is theinvented, additional determination of the magnitude of the reflection ofthe n ports in the inactive state, whereby, in the second case, thereflection magnitudes of the n ports in the inactive state can be setequal to the reflection magnitudes of the n ports in the active state.These first two designs can especially be applied with the proposedproceeding as outlined in the subordinate claim 5.

As a third design, and once again favorable in price, reference is madeto a network analyzer with four measuring positions. In this case,respectively, two of the measuring positions are directly connected withrespectively one of two inner ports of the network analyzer. As in thefirst design, the two inner ports of the network analyzer are connectedthrough a switching matrix with the n outer ports of the thus realizedmultiport network analyzer. Also, for this design, none of the knownmultiport calibration procedures can be applied.

Finally, as an additional, again rapid but very expensive alternative,attention can be called to a network analyzer, wherein the n ports,absent a connected switching matrix, are bound directly with 2·nmeasuring positions. Such a design is more closely described in the DE199 18 960 A1.

For the procedure in accord with the invention, for the two last stateddesigns, advantageously k 2-port-7-term procedures are executed. Therequirements as to calibration standards and the number is the same asthat of the DE 199 18 960 A1 known multiport calibration method, but thenumber of the contacts is different. What is new, is once again, for thedetermination of the reflection magnitudes of the n-ports in theinactive state, which determination is necessary for de-embedding,wherein, in the fourth design, the reflection magnitudes of the n portsin the active state can be set equal to the reflection magnitudes of then ports in the active state. The 10-term-procedures can, in this design,also be applied, but requires, however, high quality and more numerouscalibration standards and calibration related measurements. Thesedesigns can be applied, especially with one of the procedures proposedin the subordinate claims 6 to 8.

If, in a network analyzer, 2·n or n+1 measuring positions are provided,then the n ports can be connected directly, that means, they can beconnected by the equivalent of a throw switch with the measuringpositions. As alternative, it is possible that a switching matrix can beprovided, which has the capability of connecting each of the n ports ofthe network analyzer respectively to at least one of the measuringpositions with two inner ports of the network analyzer. The n+1 or 2·nmeasuring positions can, in this case, also be integrated in theswitching matrix. In this manner, a network analyzer requires only twoinner ports, but possesses nevertheless n+1 or 2·n measuring positions.

The claims 6 to 8 link the application of the known 7-term, 2-gatecalibration procedure with the names TAN, TNA, TRL, LLR, LRL, TAR. TMR,TRM, UMSO, TMN, LNN, TZU, TZY, TYU, LZY, ZZU, YYU, etc. where:

T=Through

R=Reflect

L=Line

A=Attenuator

M=Match

U=Unknown

S=Short

O=Open

N=Network

Z=Series Resistance

Y=Parallel Resistance.

For details of these procedures, reference is made to the dissertationpublication already mentioned above. All these algorithms belonging tothe class of the 7-term-process permit themselves, with theiradvantages, to be implemented in an invented network analyzer within theframework of the invented procedure. All of the procedures are usedk-times in their classic application form. In accord with this, each2-port standard must be contacted k-times and each 1-port standard mustbe contacted k-times. On this account, the procedure presented here,that is, the total calibration procedure departs clearly from themultiport 7-term calibration method as taught by DE 199 18 960 A1. Inthe case of multiport problems with more than three ports, procedureshave greatest interest, which procedure contains the fewest 2-portstandards, since k is much greater than n.

In the subordinate claims 7 and 8, the practically, very meaningfulusage of the 7-term procedures TRL and TMR were emphasized. In the caseof the very interesting TMR-DMV, a multitude of alternatives in thesuccession of the contacting of the 1-ports become available forselection upon the choice of the calibration standard combinations.

However, it is presupposed, that it is necessary to once connect allgates by means of a known 2-port connection (as a rule, a throughbinding T).

Further, at each port, a known impedance connection must be connected,i.e. a wave sink M, and a reflection standard R, the reflection behaviorof which, at each port must be essentially equal, or not known.

In claim 9, in an extended manner, is proposed an advantageouspossibility for the treatment of the device under test with differentialand common mode at the contact terminals. In accord with this, thedevice under test is described, instead of by the customary scatteringparameters for an unsymmetrical mode, with scattering parameters for thecommon and differential modes. The procedure distinguishes itself abovethe method used up to now with the ideal transformer, in that alldissipation mechanisms have an under-support as individual, physicallyrecoverable quantities, thus clearly providing more information to thedevelopers allowing them to improve their product in its electricalcharacteristics. With this embodiment of the invented procedure, devicessuch as SAW filter and balance devices (baluns) can be analyzed simply,quickly and in great detail.

The means of the invented circuit module are advantageously implementedin software. Further, the circuit module can show itself as astand-alone new unit or as an available component in the current networkanalyzer, wherein the said module is additionally integrated.

BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS

In the following, the invention will be described and explained ingreater detail, with the aid of the drawing. There is schematicallyshown in:

FIG. 1 a network analyzer with 3 measuring positions, 2 inner ports andn outer ports,

FIG. 2 a network analyzer with 4 measuring positions, 2 inner ports andn outer ports,

FIG. 3 a network analyzer with 3 measuring positions and n outer ports,

FIG. 4 a network analyzer with 4 measuring positions and n outer ports,

FIG. 5 a network analyzer with 2·n measuring positions and n outerports,

FIG. 6 the determination of active reflection factors in a networkanalyzer per FIG. 1

FIG. 7 the determination of inactive reflection factors in a networkanalyzer per FIG. 1, and in

FIG. 8 a block circuit diagram of a network analyzer in accord with FIG.2, for which the second error correction of dispersion parameters hasbeen made clear.

DETAILED DESCRIPTION OF THE INVENTION

First, embodiment examples of a network analyzer is described with theaid of FIGS. 1–5, which show an arrangement wherein the inventedde-embedding procedure may be applied.

FIG. 1 presents a network analyzer with three measurement positions 15,two inner ports 22 and n outer ports 11. A service and operating unit 21is connected to two inner ports 22 of the network analyzer by threemeasurement positions, namely A, B and R as well as by high frequencylines 18, 19. The two inner ports 22 are, on their own part, connectedthrough a switching module 20 with n outer ports 11. Two of themeasurement positions A and B capture back-running signals from theouter ports 11 and one of the measurement positions, i.e., R, picks upthe signals directed to the outer ports 11. The high frequency supplylines 18, 19 are used to conduct incoming signals to the outer ports 11,whereby also a (not shown) reflectometer also guides the respectivesignal to the measurement position R for the waves directed to thatpoint. The active and the inactive behavior of ports differ in thisnetwork analyzer. The twofold error correction of measured parameters ofa device under test is done in this network analyzer and in the networkanalyzers described in the following in the processing unit 21, in whichalso corresponding error terms for the first and the second correctionare determined and stored. For such a network analyzer neither the known7-term nor the 10-term multiport calibration procedure can be used. As abasis for the invented procedure, n 7-term 2-port calibration procedurecan be used, however, the 10-term 2-port calibration method is alsoacceptable.

FIG. 2 brings forth a network analyzer with four measuring positions 15,two inner ports 22 and n outer ports 11. One service and processing unit21 is connected by four measuring positions 15, namely A1, B1, A2, B2,and two high frequency feed lines 18, 19 with two inner ports 22 of thenetwork analyzer. These inner ports 22 are in electrical communicationwith a switch module 20 having n external ports 11. The high frequencylines 18, 19 emit on their own part, signals traveling to the externalports 11. Since, in this case, four measuring positions are provided, itis possible, that additionally, within the equipment, reflected wavescan be captured. The active and the inactive behavior of ports are, onceagain, different. Also, in this case, neither the known 7-term nor theknown 10-term-multiport calibration method has been applied. However, asa basis for the invented procedure, because of the possibility of thecapture of the reflected waves within the equipment, both the10-term-2-port calibration procedure as well as the 7-term 2-portcalibration procedure must be given consideration.

FIG. 3 presents, once again, a network analyzer with three measuringpositions 15 and n external ports 11. In this case, a service andprocessing unit 21 is connected by the three measuring positions 15,these being A, B, and R. The high frequency lines 18, 19 are directlybound to a switch module 20. The switch module 20 makes possible adirect connection between the measurement position 15 and the n outerports 11. Contrary to the network analyzers of the FIGS. 1 and 2, theinactive and the active behavior are identical. In this design, theknown 10-term-multiport procedure could be employed. As a basis for theinvented procedure, once more, no 7-term, 2-port calibration method canbe used, but however, again the 10-term, 2-port calibration system isacceptable.

FIG. 4 presents, similarly to the network analyzer of FIG. 3, a networkanalyzer in which the measuring positions 15 and the high frequencylines 18, 19 run directly to a switch module 20 with n outer ports 11.In FIG. 4 are provided, in any case, once again four measuring positions15, namely A1, B1, A2, B2. Alternately, also n+1 measuring positionscould be provided. As in the case of the network analyzer of FIG. 3, theinactive and the active behavior is identical. In this design, besidesthe known 10-term, multiport procedure, also the 7-term, multiportprocedure can be applied. As in the case of the network analyzer of FIG.2, as a basis for the invented procedure in addition, consideration isgiven to both the 7-term, 2-port calibration procedure as well as the10-term, 2-port calibration procedure.

Finally, in FIG. 5, we see a network analyzer, wherein a service andprocessing unit 21 is connected with 2·n measuring positions, in detail,these being A1, B1, An, Bn, and by a high frequency cable directly to aconnection module 23. This connection module 23 enables a connection ofthe measuring positions 15 with the n outer ports 11 without anyswitching action, since for each outer port 11, one measurement positionA1 to An is provided for thereto directed waves and a measuring positionB1-Bn is provided for backflow waves. As in the two network analyzersfrom FIG. 3 and FIG. 4, the inactive and the active behavior isidentical. Also, with this design, the known 10-term, multiportprocedure and the known 7-term multiport procedure can be applied. As abasis for the invented procedure, both the 7-term, 2-port calibrationprocedure and the 10-term, 2-port calibration procedure can be employed.

FIG. 6 demonstrates schematically the known determination of activereflection factors by 2-port measurings in a network analyzer such asseen in FIG. 1. FIG. 7 shows, again schematically the inventeddetermination of inactive reflection factors by 2-port measuring in anetwork analyzer such as presented in FIG. 1. In both figures, the samesection from a network analyzer with a built-in calibration standard 10is shown.

In the two FIGS. 6 and 7, one of the high frequency lines 18 isconnected through a first inner port 22 and through the switch module 20to a first outer port 11 of the n outer ports. By an inserted throughconnection 10 serving as a calibration standard, the first outer port 11is connected with a second of the n outer ports. The two ports 11 form a2-port to be measured. The second outer port 11 is, by the switch module20 and by the second inner port 22 connected with the second highfrequency supply line 19. In the switch module 20 is provided a firstswitch 24, for a switchable connection between the first inner port 22and the first outer port 11, which can connect the first inner port 22either with the first outer port 11 or to ground by means of aresistance 25. A corresponding second switch 24 is provided in theswitching module 20 for a switchable connection between the second innerport 22 and the second outer port 11. Further presented, are the threemeasuring positions 15 which are connected to the two inner ports 22.The measuring position R, in this arrangement, by means of areflectometer is capable of capturing the oncoming waves which areapproaching the first outer port 11. Similarly, the measuring position Ais likewise capable of capturing the back flowing waves from the outerport 11. The measuring position B captures the waves coming from thesecond outer port 11.

Next, the determination of active reflection factors will be explainedwith reference to FIG. 6. For the determination of the active reflectionfactors of the second outer port 11, the first outer port 11 serves as asender and the second outer port serves as a receiver. In this regard,for one thing, in the switching module 20, by means of the first switch24, a connection is established between the first inner port 22 and thefirst outer port 11, and by means of the second switch 24 a connectionis brought about between the second outer port 11 and the second innerport 22.

Subsequently, by means of the first high frequency line 18, a signal issent over the first inner port 22 and the switching module 20 onto thefirst outer port 11. As this happens, the measuring position R capturesa measured value for the signal. A portion of the approaching signal tothe first outer port 11 is immediately reflected and directed backthrough the switching module 20 and guided to the first inner port 22 ofthe measuring position A. The non-reflected part of the signal isconducted through the calibration standard 10 to the second outer port11. At this second outer port 11, another portion of the signal isreflected and travels over the first outer port 11, the switch module 20and the first inner port 22, likewise guided to the measuring positionA. The remaining residual signal is conducted over the second outer port11, the switching module 20 and the second inner port 22 on the secondhigh frequency line 19, whereby the measuring position B picks up thisportion of the signal.

In the same manner, according to connection, the second outer port 11can serve as sender, and the first outer port 11 can be the receiver, inorder that the corresponding measurement values for the activereflection factor of the first outer port 11 can be determined. Themeasurement position R is, for this purpose, is so switched, that it iscapable of capturing the waves approaching the second outer port 11.From the captured values obtained from the measurement positions 15, ina known manner, the active reflection factors of the two outer ports 11can be determined.

The determination of inactive reflection factors in the case of anetwork analyzer, wherein the active and inactive behaviors aredifferent, will now be explained with reference to FIG. 7. Such adetermination is not known in conventional calibration procedures. Forthe determination of the inactive reflection factors, once again, at thebeginning the first outer port 11 plays the role of sender, the secondouter port, on the other hand is shut off. For the shutting off, in theswitching module 20, the second switch 24 is so positioned, that itconnects the second outer port 11 with the second resistance 25 insteadof with the second inner port 22.

Under these circumstances, then a renewed signal is sent over the firsthigh frequency line 18 to the first outer port 11. A first portion ofthe signal is again reflected to the first outer port 11 and anadditional portion is sent to the second outer port 11. The secondreflected portion differentiates itself however, from the secondreflected portion of the signal in FIG. 6, since the signal at thesecond outer port 11 now, because of the changed position of the secondswitch 24 is directed to a terminal resistance 25, instead of throughthe second inner port 22 on the second high frequency line 19.

The capture of the approaching and the reflected waves corresponds tothat shown in FIG. 6, only that in this case, that is, no signal reachesthe measurement position B, since the connection to this measurementposition has be interrupted. However, from the measured values at themeasurement positions A and R, now a reflection factor for the secondouter port 11 in the inactive state can be determined. Additionally, thedetermined inactive reflection factor, with the availability of themeasurement values for the active reflection factors, can be subjectedto an error correction, in order to set aside the influence of thecalibration standard 10 between the outer ports 11 from the saidreflection factor.

For the determination of the reflection factor for the first measurementposition 11 in the inactive state, the procedure is renewed in theopposite direction and carried out with inverted switch positioning.

The general problem of n-ports is often reduced to 3-ports for the sakeof clarity. Likewise, FIG. 8 shows, for example, a 3-port multi-portnetwork analyzer. The multi-port network analyzer in the figure,corresponds to that in the introductory passages of the description asan already mentioned third practical, relevant design network analyzer,that is, the network analyzer of FIG. 2.

The network analyzer of FIG. 8 possesses a signal source 17, which isconnected to a real switch 15 with two branches, 18, 19. Each of theline branches 18, 19 is respectively assigned to connections, which aretwo assumed ideal measurement positions 15, namely, m1, m2, or m3, m4.Both conductor lines 18, 19 can be electrically joined through an innerport 22 and a common switching matrix 20 by likewise assumed idealswitches with one optional selection of first error network 12, seconderror network 13, and third error network 14. The switching matrix 20represents herein, the real switching module from FIG. 2. Each of thethree error networks 12, 13, 14 is finally connected with a port 11 witha measured DUT 10 (DUT=Device Under Test=measured object). The deviceunder test can, in one instance, be an object, the reflection parametersand transmission parameters of which are to be determined. Additionally,various calibration standards are applied for the error-correction ofdetermined scattering parameters.

When a signal, the characteristics of which, such as reproducibility,durable stability, etc., are not yet exact, is emitted from source 17,it enters a switch module 16 and is diverted to one of the two linebranches 18, 19, by which it is conducted to an inner port 22. By meansof the switching matrix 20, the signals to the ports 11 of the deviceunder test 10, after a reflection to, or a transmission through, saidmeasured device 10, the signals are returned again back to the linebranches 18, 19. The waves which are approaching the device under test10 are designated with a₁, a₂, a₃ and the waves departing from thedevice under test 10 are designated b₁, b₂, b₃, whereby the same indexis assigned to the corresponding port 1, 2, 3. The accumulated errors ofthe switching matrix 20, the measurement positions 15, and theconnection cable 18, 19 are combined in the respective error-matrices ofthe error-network 12–14.

For the determination of the scattering parameters of a connected deviceunder test 10, one of the measurement positions m₂ or m₃ takes a measureat one of the line branches 18, 19 for the approaching wave, and themeasurement positions m₁, m₄ take at the corresponding line branch 19,18 a measurement for the back fed, rejected or transmitted waves.

Next, the network analyzer is subjected to a 7-term 2-port calibrationprocedure, in order to make available error-terms for a first errorcorrection of scattering parameters. Corresponding to the description inrespect to FIG. 7, then for a second error-corrective measure, theerror-free reflection factors r_(ii)(1=1−3) of the three ports aredetermined in the inactive state, where i=1 is assigned to the firstport, i=2 is assigned to the second port and i=3 is assigned to thethird port.

In this connection, it is possible for a device under test to have thescattering parameters determined as rough measured values and an initialerror correction to be undertaken on the basis of the error-term of the7-term, 2-port calibration procedure. The measured and one-timecorrected scattering parameters build the nine values of a 3×3scattering matrix and are designated by: s_(ij) ^(m) where (i=row 1–3;j=column 1–3).

From the one-time corrected scattering parameters of the device undertest, and the inventively determined and error-free reflection factorsr_(ii) it is now possible to determine the “true” scattering matrix [S]of the device under test 10 with three measuring ports 11 in theequation:

$\begin{matrix}{\begin{pmatrix}b_{1} \\b_{2} \\b_{3}\end{pmatrix} = {\underset{\underset{\lbrack S\rbrack}{︸}}{\begin{pmatrix}S_{11} & S_{12} & S_{13} \\S_{21} & S_{22} & S_{23} \\S_{31} & S_{32} & S_{33}\end{pmatrix}}\begin{pmatrix}a_{1} \\a_{2} \\a_{3}\end{pmatrix}}} & (1)\end{matrix}$It is now permissible to simply formulate, for a 3-portmulti-port-network-analyzer, by the known signal-flow method, theequations for the de-embedded scattering parameters, as follows:

$\begin{matrix}{S_{11} = {S_{11}^{m} - {S_{13}^{m}S_{31}^{m}\frac{r_{33}}{1 - {r_{33}S_{33}^{m}}}} - {S_{12}^{m}S_{21}^{m}\frac{r_{22}}{1 - {r_{22}S_{22}^{m}}}}}} & (2) \\{S_{22} = {S_{22}^{m} - {S_{12}^{m}S_{21}^{m}\frac{r_{11}}{1 - {r_{11}S_{11}^{m}}}} - {S_{23}^{m}S_{32}^{m}\frac{r_{33}}{1 - {r_{33}S_{33}^{m}}}}}} & (3) \\{S_{33} = {S_{33}^{m} - {S_{13}^{m}S_{31}^{m}\frac{r_{11}}{1 - {r_{11}S_{11}^{m}}}} - {S_{23}^{m}S_{32}^{m}\frac{r_{22}}{1 - {r_{22}S_{22}^{m}}}}}} & (4) \\{S_{12} = {S_{12}^{m} - {S_{32}^{m}S_{13}^{m}\frac{r_{33}}{1 - {r_{33}S_{33}^{m}}}}}} & (5) \\{S_{13} = {S_{13}^{m} - {S_{12}^{m}S_{23}^{m}\frac{r_{22}}{1 - {r_{22}S_{22}^{m}}}}}} & (6) \\{S_{21} = {S_{21}^{m} - {S_{31}^{m}S_{23}^{m}\frac{r_{33}}{1 - {r_{33}S_{33}^{m}}}}}} & (7) \\{S_{23} = {S_{23}^{m} - {S_{13}^{m}S_{21}^{m}\frac{r_{11}}{1 - {r_{11}S_{11}^{m}}}}}} & (8) \\{S_{31} = {S_{31}^{m} - {S_{32}^{m}S_{21}^{m}\frac{r_{22}}{1 - {r_{22}S_{22}^{m}}}}}} & (9) \\{S_{32} = {S_{32}^{m} - {S_{31}^{m}S_{12}^{m}\frac{r_{11}}{1 - {r_{11}S_{11}^{m}}}}}} & (10)\end{matrix}$Likewise, the equations for an n-port can be determined, whereby theterms of higher orders are generated, which contain two and morer_(ii)—values. These can, however, be disregarded by good approximationapproaches, since the r_(ii)—values are small, so that each correctioncomputation is given in the form of the solution found under equation(2). For example, for a 4-port, we have:

$\begin{matrix}{S_{11} = {S_{11}^{m} - {S_{13}^{m}S_{31}^{m}\frac{r_{33}}{1 - {r_{33}S_{33}^{m}}}} - {S_{12}^{m}S_{21}^{m}\frac{r_{22}}{1 - {r_{22}S_{22}^{m}}}}}} & (11)\end{matrix}$

In the following, it shall now be presented, how, with the availabilityof the determined scattering parameter values of a 3-port, the multimodevalue of a 2-port, which encompasses an unsymmetrical entry as well as atwo conductor line system, by which a common and a differential modeoccur, can be obtained. The 2-port, with the unsymmetrical entry can be,for example, a micro strip line and the two-line system, for instancecan be a two-line system with two parallel micro strips.

This procedure is especially of interest where SAW-filter andsymmetrical members are concerned, since here, in contrast to the knownprocedure, the loss mechanisms are separated.

The unsymmetrical port is in FIG. 8 the port 1 with the incoming wavea₁, and the departing wave b₁. The two other ports for the two-linesystem are the ports 2 and 3 with the wave magnitudes a₂, a₃, b₂, b₃.The de-embedded dispersion for the three ports is given.

On the two-line system, occur a common mode wave and a differential modewave, which can be described with the values: a₂ ⁺, a₂ ⁻, b₂ ⁺, b₃ ⁻.The key for the multimode computation is now, that in a linear system,the mode of the unsymmetrical measurement system allows itself to bejoined with the two-line system, as follows:

$\begin{matrix}{a_{2}^{+} = {\frac{1}{\sqrt{2}}\left( {a_{2} + a_{3}} \right)}} & (12) \\{a_{2}^{-} = {\frac{1}{\sqrt{2}}\left( {a_{2} + a_{3}} \right)}} & (13) \\{b_{2}^{+} = {\frac{1}{\sqrt{2}}\left( {b_{2} + b_{3}} \right)}} & (14) \\{b_{2}^{-} = {\frac{1}{\sqrt{2}}\left( {b_{2} + b_{3}} \right)}} & (15)\end{matrix}$

If one evaluates the equations and defines new scattering parametersfrom the usual topography with the wave magnitudes a and b, but with themode-considerations, whereby an “0” designates the unsymmetrical mode,then there arises the following nine scattering parameters for the2-port with the unsymmetrical entry and the symmetrical exit.

The intrinsic parameter for the unsymmetrical mode:S ₁₁ =S ₁₁  (16)

The intrinsic parameter for the common mode:

$\begin{matrix}{S_{22}^{+} = {\frac{1}{2}\left( {S_{22} + S_{23} + S_{32} + S_{33}} \right)}} & (17)\end{matrix}$

Intrinsic parameter for the differential mode:

$\begin{matrix}{S_{22}^{-} = {\frac{1}{2}\left( {S_{22} - S_{23} - S_{32} - S_{33}} \right)}} & (18)\end{matrix}$

Conversion parameter for the common mode in the unsymmetrical mode:

$\begin{matrix}{S_{12}^{+ 0} = {\frac{1}{\sqrt{2}}\left( {S_{12} + S_{13}} \right)}} & (19)\end{matrix}$

Conversion parameter for the differential mode in the symmetrical mode:

$\begin{matrix}{S_{12}^{- 0} = {\frac{1}{\sqrt{2}}\left( {S_{12} - S_{13}} \right)}} & (20)\end{matrix}$

Conversion parameter for the unsymmetrical mode in the common mode

$\begin{matrix}{S_{21}^{0 +} = {\frac{1}{\sqrt{2}}\left( {S_{21} + S_{31}} \right)}} & (21)\end{matrix}$

Conversion parameter for the unsymmetrical mode in the differentialmode:

$\begin{matrix}{S_{21}^{0 -} = {\frac{1}{\sqrt{2}}\left( {S_{21} - S_{31}} \right)}} & (22)\end{matrix}$

Conversion parameter for the common mode in the differential mode:

$\begin{matrix}{S_{22}^{+ -} = {\frac{1}{2}\left( {S_{22} + S_{23} - S_{32} - S_{33}} \right)}} & (23)\end{matrix}$

Conversion parameter for the differential mode in the common mode:

$\begin{matrix}{S_{22}^{- +} = {\frac{1}{2}\left( {S_{22} - S_{23} + S_{32} - S_{33}} \right)}} & (24)\end{matrix}$Even when the somewhat more closely carried out description of a deviceunder test with unsymmetrical modes by means of separate scatteringparameters for the common and the differential modes, is based here onthe invented corrected scattering parameters, it is also possible thatan application of this or a corresponding description could be based onscattering parameters otherwise determined.

1. A process for correcting errors by de-embedding of scatteringparameters measured with an n ports comprising vector network analyzer,of a device under test connected with the ports, said processcomprising: performing up to $k = {n \cdot \frac{n - 1}{2}}$ 2-portcalibrations on different calibration standards switched onto the portsin an active state in optional succession as a basis for a first errorcorrection of measured scattering parameters of a device under test,wherein n is an integer greater than 1; and determination of reflectionparameters of at least some of the n ports in an inactive state with theavailability of results from 2-port measurements on at least onecalibration standard switched onto the ports in the active state and/orthe inactive state as a basis for a second error correction of at leasta part of the measured scattering parameters corrected with the firsterror correction of the device under test.
 2. The process of claim 1,wherein the determination of the reflection parameters of at least apart of the n ports is carried out with the up to k 2-port calibrations,which became available in measuring steps for the first errorcorrection.
 3. The process of claim 1, wherein the reflection parametersof all n ports are determined in the inactive state.
 4. The process ofclaim 1, wherein in a further step, to determine the scatteringparameters of a device under test, the scattering parameters are subjectto a first error correction on the basis of the up to k 2-portcalibrations, and the thus corrected scattering parameters, at leastpartially, undergo a second error correction on the basis of thedetermined reflection parameters of ports in the inactive state.
 5. Theprocess of claim 1, wherein the network analyzer for the measurement ofthe calibration standard possesses at least three measurement positionsconnected with, or connectable to, the ports and by which networkanalyzer, in combination with available coaxial or planar calibrationstandards for the 2-port calibrations as a basis for a first errorcorrection, the following steps are realized and carried out: first, upto k calibration measurements are taken on respectively one 2-port,which is realized by means of the direct connection of two ports, or bymeans of a short matching line of known length and of known damping,which said line is connected between the k possible port combinations, afurther calibration measurement is made on an n−1-port, which isrealized by means of n known impedances, and a further calibrationmeasurement is made on an n−1-port, which is realized by means of nknown short circuits, and an additional calibration measurement is madeon an n−1-port, which is realized by means of n known open circuits,whereby the value of the parameter n represents the number n of theports.
 6. The process of claim 1, wherein the network analyzer for themeasurement of the calibration standards possesses at least fourmeasurement positions connected to, or connectable to, the ports, andwherein in combination with available coaxial or planar calibrationstandards, as a basis for the first error correction the calibrationstandards of all known 7-term procedures between the ports in all kpossible combinations are measured in optional succession.
 7. Theprocess of claim 1, wherein the network analyzer for the measurement ofthe calibration standards possesses at least four measurement positionsconnectable to, or connected to the ports and wherein in combinationwith available coaxial or planar calibration standards as a basis forthe first error correction, the following steps are realized and carriedout: first up to k calibration measurements are made on respectively one2-port, which is realized by means of the direct connection of theports, or by means of a short matching line of known length and knowntransmission characteristics which said line is connected between the kpossible port combinations, further additional calibration measurementsare made on respectively one 2-port, which is realized by means of ashort, matching line of unknown length and with unknown transmissioncharacterizations, wherein the line is connected between the possible kport combinations, and a further calibration measurement is made on ann−1-port, which is realized by means of n non-ideal short circuits oropen circuits whereby the value of the parameter n represents the numbern of the ports.
 8. The process of claim 1, wherein the network analyzerfor the measurement of the calibration standards possesses at least fourmeasuring positions connected to, or connectable to, the ports, andwherein, in combination with available coaxial or planar calibrationstandards as a basis for a first error correction, the following stepsare realized and carried out: the up to k calibration measurements aremade on respectively one 2-port, which is realized by means of thedirect connection of the ports or by a short matching line of knownlength and known transmission characteristics, which said line isconnected between the k possible port combinations, a furthercalibration measurement is made on a n−1-port, which is realized bymeans n-known impedances, and an additional calibration measurement ismade on a n−1-port, which is realized by means of n, non-ideal, shortcircuits or open circuits whereby the value of the parameter nrepresents the number n of the ports.
 9. The process of claim 1, withthe usage of known coaxial or planar calibration standards, and whichprocedure further comprises the steps: measuring the scatteringparameters of a device under test which exhibits symmetrical andunsymmetrical modes and which device under test is connected with theports of the network analyzer, correcting the measured scatteringparameters with a first error correction on the basis of the up to k2-port calibrations and a second error correction on the basis of thedetermined reflection parameters, resulting in two-fold correctedscattering parameters Sij, where i,j=1 to n, whereby the respectivesecond index identifies the port, through which a respective wave isentered in the device under test, and the respective first indexidentifies the port, through which the respective wave departs from thesaid device under test, and the determining of separate scatteringparameters for the common and the differential mode of the device undertest from the measured and two-fold corrected scattering parametersS_(ij), whereby, for a symmetrical exit of the device under testconnected to an arbitrary port i and j, the intrinsic parameters for thecommon mode are determined to$\frac{1}{2}\left( {S_{ii} + S_{ij} + S_{ji} + S_{jj}} \right)$ and theintrinsic parameters for the differential mode are determined to$\frac{1}{2}\left( {S_{ii} - S_{ij} - S_{ji} + S_{jj}} \right)$ theconversion parameters for the common mode in the differential mode aredetermined to${\frac{1}{2}\left( {S_{ii} + S_{ij} - S_{ji} - S_{jj}} \right)},$ andthe conversion parameters for the differential mode in the common modeare determined to$\frac{1}{2}{\left( {S_{ii} - S_{ij} + S_{ji} - S_{jj}} \right).}$
 10. Avector network analyzer for the determination of the scatteringparameters of a device under test, with n ports for the connection ofthe device under test and calibration standards as well as having atleast 3 measuring positions, whereby each port is connected with, orconnectable to at least one measuring position for the capture of wavemagnitudes of signals approaching the port and connected with, orconnectable to a measuring position for the capture of wave magnitudesof signals departing from the port as well as processing means for thecarrying out of the process of claim
 1. 11. The vector network analyzerof claim 10 with exactly three measuring positions, characterized by twoinner ports connected through a switch with said three measuringpositions and a switch module, which has the capability of connectingthe n-ports through the two inner ports with the said three measuringpositions.
 12. The vector network analyzer of claim 10 with exactly fourmeasuring position, characterized by two inner ports connected with twoof the four measuring positions and a switch module, which has thecapability of connecting the n ports through the two inner ports withthe four measuring positions.
 13. The vector network analyzer of claim10 with n+1 measuring positions characterized by one switch module, bymeans of which each of the n ports can be, or is, respectively directlyconnected at least with one of the n+1 measuring positions.
 14. Thevector network analyzer of claim 10, with 2·n measuring positionscharacterized in that, each of the n ports is directly connected withrespectively two of the 2·n measuring positions.